Question : M is the incentre of the $\triangle $XYZ. If $\angle $YXZ + $\angle $YMZ = 150°, then what is the value of $\angle $YXZ?
Option 1: 40°
Option 2: 55°
Option 3: 60°
Option 4: 45°
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Correct Answer: 40°
Solution :
$\angle $YXZ + $\angle $YMZ = 150°
⇒ $\angle $YMZ = 150° – $\angle $YXZ
M is the incentre,
⇒ $\angle $YMZ = 90° + $\frac{1}{2}\angle $YXZ
⇒ 150° – $\angle $YXZ = 90° + $\frac{1}{2}\angle $YXZ
⇒ 60° = $\frac{3}{2}\angle $YXZ
⇒ $\angle $YXZ = 40°
Hence, the correct answer is 40°.
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